What is the weight of a balloon filled with air?

[utkarshakash]

Homework Statement

The weight of an empty balloon on a spring balance is w1. The weight becomes w2 when the balloon is filled with air. Let the weight of the air itself be w. Neglect the thickness of the balloon when it is filled with air. Also neglect the difference in the densities of air inside and outside the balloon

a)w2=w1
b)w2=w1+w
c)w2<w1+w
d)w2>w1

Homework Equations

The Attempt at a Solution

In my opinion it should be b). I have simply added the weights. But the correct answer is a) and c).

 

[haruspex]

The wording of the question is rather misleading. You have to realize that when it discusses the weights of the balloon (with and without air) it means something different from when it mentions the weight of the air itself.
For the balloon, both w1 and w2 refer to the reading you will get from the spring balance. The question ought to make clear this is in a surrounding of air, not in a vacuum. If you were to weigh the air the same way (maybe in some magical weightless sac), the spring balance would show zero, right? So when they say the air ways w, they don't mean as shown on the spring balance - they mean the actual force exerted on it by gravity.
Does that help?

 

[utkarshakash]

The wording of the question is rather misleading. You have to realize that when it discusses the weights of the balloon (with and without air) it means something different from when it mentions the weight of the air itself.
For the balloon, both w1 and w2 refer to the reading you will get from the spring balance. The question ought to make clear this is in a surrounding of air, not in a vacuum. If you were to weigh the air the same way (maybe in some magical weightless sac), the spring balance would show zero, right? So when they say the air ways w, they don't mean as shown on the spring balance - they mean the actual force exerted on it by gravity.
Does that help?

It is still unclear to me.

 

[haruspex]

I hope you weren't thrown by this typo in my previous post:

"So when they say the air ways w"​

I meant, of course, "So when they say the air weighs w"

If I hang on object from a spring balance, and the spring shows a weight of X, I say the object weighs X, right? But that is not exactly equal to the force exerted on it by Earth's gravity. Why?

 

[utkarshakash]

I hope you weren't thrown by this typo in my previous post:
If I hang on object from a spring balance, and the spring shows a weight of X, I say the object weighs X, right? But that is not exactly equal to the force exerted on it by Earth's gravity. Why?

I did not know this earlier. Thanks for pointing out.

 

[haruspex]

I did not know this earlier. Thanks for pointing out.

But do you understand why it is not quite the same? (Hint: it's to do with the air.)

 

[utkarshakash]

But do you understand why it is not quite the same? (Hint: it's to do with the air.)

The air exerts an upward force on it.

 

[haruspex]

The air exerts an upward force on it.

Exactly. So the weights given for the balloon, w1 and w2, are as measured by the spring balance. But the weight given for the air, w, cannot be; it must be the actual gravitational pull. Can you see how that makes a) and c) right?

 

[utkarshakash]

Exactly. So the weights given for the balloon, w1 and w2, are as measured by the spring balance. But the weight given for the air, w, cannot be; it must be the actual gravitational pull. Can you see how that makes a) and c) right?

Yes. Thanks!